## Math 285. Differential Equations

Syllabus for Instructors

**Text: ****Elementary Differential Equations and Boundary Value Problems. 10th Edition, Boyce & DiPrima, Wiley**

**Chapter 1: Introduction**

1.1: Some Basic Mathematical Models; Direction Fields (1)

1.2: Solutions of Some Differential Equations (1)

1.3: Classification of Differential Equations (1)

1.4: Historical Remarks (Assign for reading only)

**Chapter 2: First Order Differential Equations**

2.1: Linear Equations; Method of Integrating Factors (2)

2.2: Separable Equations (1)

2.3: Modeling with First Order Equations (Optional?)

2.4: Differences Between Linear and Nonlinear Equations (1) (Cover Bernoulli equation in the problems)

2.5: Autonomous Equations and Population Dynamics (2)

2.6: Exact Equations and Integrating Factors (Optional. We de-emphasized this in the past)

2.7: Numerical Approximations: Euler's Method (Assign as reading)

2.8: The Existence and Uniqueness Theorem (This is the proof. Optional)

2.9: First Order Difference Equations (Skip)

2.M: Miscellaneous Problems (1) (Work through some reducible second order equations)

**Chapter 3: Second Order Linear Equations**

3.1: Homogeneous Equations with Constant Coefficients (1)

3.2: Solutions of Linear Homogeneous Equations; the Wronskian (1)

3.3: Complex Roots of the Characteristic Equations (1)

3.4: Repeated Roots; Reduction of Order (1)

3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients (1)

3.6: Variation of Parameters (1)

3.7: Mechanical and Electrical Vibrations (2)

3.8: Forced Vibrations (2)

**Chapter 4: Higher Order Linear Equations**

4.1: General Theory of nth Order Linear Equations (1)

4.2: Homogeneous Equations with Constant Coefficients (1)

4.3: The Method of Undetermined Coefficients (1)

4.4: The Method of Variation of Parameters (Optional)

**Chapter 10: Partial Differential Equations and Fourier Series**

10.1: Two-Point Boundary Value Problems (3)

10.2: Fourier Series (2)

10.3: The Fourier Convergence Theorem (1)

10.4: Even and Odd Functions (1)

10.5: Separation of Variables; Heat Conduction in a Rod (1)

10.6: Other Heat Conduction Problems (1)

10.7: The Wave Equation: Vibrations of an Elastic String (2)

10.8: Laplace's Equation (2)

**Chapter 11: Boundary Value Problems and Sturm-Liouville Theory**

11.1: The Occurrence of Two-Point Boundary Value Problems (1)

11.2: SturmÐLiouville Boundary Value Problems (1) (Skip the proofs)

11.3: Nonhomogeneous Boundary Value Problems (Skip)

11.4: Singular SturmÐLiouville Problems (Skip)

11.5: Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion (Skip)

11.6: Series of Orthogonal Functions: Mean Convergence (Skip)

**Exams, review, and leeway (6 lectures)**

**Total: 44 lectures**

updated 8/16/17